Circulatory Fidelity began as a diagnostic for variational inference failure and grew into a unified framework for measuring relational structure across scientific domains. It is an independent research program in active development.
The core insight is simple: the whole is sometimes more than the sum of its parts, and when you factorize a system into independent parts you pay an information-theoretic cost proportional to that "more" you discarded. IC (Inference Coupling) measures this cost from model structure alone, before inference.
What started as a single metric for a single problem, detecting when mean-field variational inference would fail, turned out to connect to information geometry, thermodynamics, quantum information, spectral graph theory, and dozens of other domains. These connections aren't analogies. The same mathematical objects show up independently in each field, measured by the same IC.
CF rests on an explicit commitment to relational primacy: relations are primary, and nodes emerge from them. That's not decorative philosophy. It generates specific predictions, confirmed by exact mathematical results, controlled simulation, and real-world public datasets, each held to its own standard of evidence rather than pooled into one tally.
CF v1.1 is published on Zenodo (DOI: 10.5281/zenodo.18237471). Three papers are in preparation for simultaneous arXiv release. The framework spans … domains across two tiers of validation strength, with … formally characterized cross-domain connections.
The framework emerged from studying where Bayesian computation fails, specifically mean-field variational inference applied to systems with significant coupling. The diagnostic question "when does factorization cost too much?" turned out to have answers far beyond the inference context where it was first asked.
Three papers are in preparation for simultaneous arXiv release. Each stands alone for its target audience while cross-referencing the others for depth.
Core MFVI diagnostic: IC definition, the Relational Invariance theorem, validation studies, practical workflow. For Bayesian practitioners who need to know when their factorized inference will fail.
Control Coupling taxonomy, observer-dependence, and screening effects. How coupling strength varies by layer depth, and why the nearest layer always dominates. For researchers working with deep hierarchical models.
Detection of higher-order relational structure invisible to pairwise analysis. Walsh-Hadamard protocol, encoding-relativity, and the GF(2)–stabilizer correspondence. For anyone working with systems where pairwise methods fail unexpectedly.
The research is conducted within a distributed laboratory architecture spanning … domains across two tiers of validation strength. Each domain maintains its own state, operationalization, and validation pipeline. The network of … cross-domain connections is formally characterized. Each one is demonstrated through shared mathematical structure, not asserted by analogy.
From variational inference and information geometry (Tier 1, fully validated) through cognitive science, bioelectric theory, and water-network dynamics (Tier 2, structurally established). Each domain is classified by a composite score reflecting formal, empirical, and operational soundness.
Connections between domains are not hand-waved analogies. Each edge represents shared mathematical objects (the same IC, the same geodesic coordinate, the same cost function) appearing independently in each domain. The stabilizer/coset decomposition separates what transfers between domains (IC values, coupling regime, cost function: the universal structure) from what is domain-specific (node identity, measurement protocol, physical interpretation, reconstructed locally in each field).
Every claim within the laboratory carries an explicit STQA class (proven, structural, analogical) and pipeline stage (substrate, computed, predicted, confirmed). Mathematical identities are never conflated with empirical claims; structural correspondences are never confused with casual analogies.
Explore the full domain network on the Domains page.
Reference implementations in Python and Julia are available in the project repository (linked below), MIT licensed. The snippets below illustrate the diagnostic API.
from circulatory_fidelity import inference_coupling, diagnose # Estimate IC between latent and observed ic, se = inference_coupling(z_samples, x_samples) # Full diagnostic workflow result = diagnose(z, x, model_type='filtering') print(f"IC = {result['ic']:.3f}") print(f"Risk: {result['risk_level']}") print(f"MSE ratio: {result['mse_ratio']:.2f}")
using CirculatoryFidelity # Estimate IC from samples ic, se = inference_coupling(z, x) # Closed-form for Gaussian systems ic = ic_gaussian(ρ) # Two-stage coplexity detection result = two_stage_protocol(X, y) println("Pairwise IC: $(result.ic2)") println("Coplex IC: $(result.ic3)")
CF is in active development. Collaboration inquiries, technical questions, domain extension proposals, and critical engagement are welcome.